Systems and methods for estimating hemodynamic forces acting on plaque and monitoring patient risk

ABSTRACT

Computer-implemented methods are disclosed for estimating values of hemodynamic forces acting on plaque or lesions. One method includes: receiving one or more patient-specific parameters of at least a portion of a patient&#39;s vasculature that is prone to plaque progression, rupture, or erosion; constructing a patient-specific geometric model of at least a portion of a patient&#39;s vasculature that is prone to plaque progression, rupture, or erosion, using the received one or more patient-specific parameters; estimating, using one or more processors, the values of hemodynamic forces at one or more points on the patient-specific geometric model, using the patient-specific parameters and geometric model by measuring, deriving, or obtaining one or more of a pressure gradient and a radius gradient; and outputting the estimated values of hemodynamic forces to an electronic storage medium. Systems and computer readable media for executing these methods are also disclosed.

RELATED APPLICATION(S)

This application claims priority to U.S. Provisional Application No.62/192,314 filed Jul. 14, 2015, the entire disclosure of which is herebyincorporated herein by reference in its entirety.

FIELD OF THE DISCLOSURE

Various embodiments of the present disclosure relate generally tomedical imaging, health risk monitoring, and related methods. Morespecifically, particular embodiments of the present disclosure relate tosystems and methods for estimating hemodynamic forces acting on plaque,and monitoring risk.

BACKGROUND

Atherosclerosis is a specific form of arteriosclerosis, caused bythickening artery walls and plaque formation. Hemodynamic forces,including wall shear stress (WSS) and axial plaque stress (APS), mayaffect the pathogenesis of coronary atherosclerosis. In particular, wallshear stress may affect the progression of coronary plaques, while axialplaque stress (APS), which is the axial component of traction, mayinfluence the risk of plaque rupture. Since these hemodynamic parametersmay have unique characteristics in lesions as compared to conventionalmetrics, e.g., lesion severity or fractional flow reserve (FFR),considering these hemodynamic forces in the clinical decision-makingprocess may improve the risk stratification of plaques and ultimatelyhelp patient care.

Axial plaque stress may correlate to radius gradient in a patient'svascular geometry. Radius gradient may incorporate clinically relevantgeometric parameters, including lesion length, minimum lumen area, andstenosis severity. Thus, a desire exists for a method of providing apatient-specific evaluation of axial plaque stress and radius gradientto provide improved treatment strategies for vascular disease.Furthermore, a desire exists for a method of monitoring hemodynamicparameters (e.g., axial plaque stress, radius gradient, etc.) fordischarged outpatients in order to provide continued personalized care.

SUMMARY

The foregoing general description and the following detailed descriptionare exemplary and explanatory only and are not restrictive of thedisclosure. According to certain aspects of the present disclosure,systems and methods are disclosed for estimating values of hemodynamicforces acting on plaque or lesions.

One method includes: receiving one or more patient-specific parametersof at least a portion of a patient's vasculature that is prone to plaqueprogression, rupture, or erosion; constructing a patient-specificgeometric model of at least a portion of a patient's vasculature that isprone to plaque progression, rupture, or erosion, using the received oneor more patient-specific parameters; estimating, using one or moreprocessors, the values of hemodynamic forces at one or more points onthe patient-specific geometric model, using the patient-specificparameters and geometric model by measuring, deriving, or obtaining oneor more of a pressure gradient and a radius gradient; and outputting theestimated values of hemodynamic forces to an electronic storage medium.

In accordance with another embodiment, a system for estimating values ofhemodynamic forces acting on plaque or lesions comprises: a data storagedevice storing instructions for estimating values of hemodynamic forces;and a processor configured for: receiving one or more patient-specificparameters of at least a portion of a patient's vasculature that isprone to plaque progression, rupture, or erosion; constructing apatient-specific geometric model of at least a portion of a patient'svasculature that is prone to plaque progression, rupture, or erosion,using the received one or more patient-specific parameters; estimating,using one or more processors, the values of hemodynamic forces at one ormore points on the patient-specific geometric model, using thepatient-specific parameters and geometric model by measuring, deriving,or obtaining one or more of a pressure gradient and a radius gradient;and outputting the estimated values of hemodynamic forces to anelectronic storage medium.

In accordance with another embodiment, a non-transitory computerreadable medium for use on a computer system containingcomputer-executable programming instructions for performing a method ofestimating values of hemodynamic forces acting on plaque or lesions, themethod comprising: receiving one or more patient-specific parameters ofat least a portion of a patient's vasculature that is prone to plaqueprogression, rupture, or erosion; constructing a patient-specificgeometric model of at least a portion of a patient's vasculature that isprone to plaque progression, rupture, or erosion, using the received oneor more patient-specific parameters; estimating, using one or moreprocessors, the values of hemodynamic forces at one or more points onthe patient-specific geometric model, using the patient-specificparameters and geometric model by measuring, deriving, or obtaining oneor more of a pressure gradient and a radius gradient; and outputting theestimated values of hemodynamic forces to an electronic storage medium.

Additional objects and advantages of the disclosed embodiments will beset forth in part in the description that follows, and in part will beapparent from the description, or may be learned by practice of thedisclosed embodiments. The objects and advantages of the disclosedembodiments will be realized and attained by means of the elements andcombinations particularly pointed out in the appended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the disclosed embodiments, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate various exemplary embodiments,and together with the description, serve to explain the principles ofthe disclosed embodiments.

FIG. 1 is a block diagram of an exemplary system and network forestimating hemodynamic forces acting on plaque and monitoring risk,according to an exemplary embodiment of the present disclosure.

FIG. 2A depicts pictorial and graphical diagrams of hemodynamic forcesacting on plaque, according to an exemplary embodiment of the presentdisclosure.

FIG. 2B depicts graphical diagrams and equations illustrating therelationship between hemodynamic forces acting on plaque, according toan exemplary embodiment of the present disclosure.

FIG. 3 is a block diagram of a general method of estimating the valuesof hemodynamic forces acting on plaque and monitoring risk, according toan exemplary embodiment of the present disclosure.

FIG. 4 is a block diagram of an exemplary method of estimating thevalues of hemodynamic forces acting on plaque and monitoring risk, usingnon-invasive imaging and computational fluid dynamics, according to anexemplary embodiment of the present disclosure.

FIG. 5 is a block diagram of an exemplary method of acquiring apatient-specific geometric model non-invasively (e.g., through coronarycomputerized tomography angiography (cCTA), according to an exemplaryembodiment of the present disclosure. FIG. 5 may depict an exemplarymethod of performing step 302 of method 300 in FIG. 3 and/or step 402 ofmethod 400 in FIG. 4.

FIG. 6 is a block diagram of an exemplary method of usingpatient-specific parameters to output the values of hemodynamic forces,using computational fluid dynamics, according to an exemplary embodimentof the present disclosure. FIG. 6 may depict an exemplary method ofperforming step 306 of method 300 in FIG. 3 and/or step 408 of method400 in FIG. 4.

FIGS. 7, 8, and 9 are block diagrams of exemplary methods of estimatingthe values of hemodynamic forces acting on plaque and monitoring risk,using a machine learning algorithm to estimate values of hemodynamicforces, according to an exemplary embodiment of the present disclosure.

FIG. 7 may depict an exemplary method for training a machine learningalgorithm for estimating values of hemodynamic forces, usingnon-invasive imaging and computational fluid dynamics.

FIG. 8 may depict an exemplary method of applying a trained machinelearning algorithm to estimate values of hemodynamic forces, using anon-invasively acquired geometric model of a target patient.

FIG. 9 may depict an exemplary method of applying a trained machinelearning algorithm to estimate values of hemodynamic forces, using aninvasively acquired geometric model of a target patient.

FIG. 10 is a block diagram of an exemplary method of training andapplying a machine learning algorithm using patient-specific parametersto output values of hemodynamic forces, according to an exemplaryembodiment of the present disclosure. FIG. 10 may depict an exemplarymethod of performing steps 710 and 712 of method 700 in FIG. 7, step 808of method 800 in FIG. 8, and/or step 908 of method 900 in FIG. 9.

FIGS. 11A and 11B are block diagrams of exemplary methods, 1100A and1100B, respectively, for using the estimated values of hemodynamicforces to monitor risk and make appropriate clinical decisions,according to an exemplary embodiment of the present disclosure.

FIG. 12 is a block diagram of exemplary method 1200 for determining anexercise intensity using estimated values of hemodynamic forces based ona simulated or performed exercise and/or stress test, according to anexemplary embodiment of the present disclosure.

FIG. 13 is a block diagram of exemplary method 1300 for usingpredetermined exercise intensity (e.g., as in FIG. 12) to monitor riskin patients, according to an exemplary embodiment of the presentdisclosure.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the exemplary embodiments of thedisclosure, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts.

Atherosclerosis is a specific form of arteriosclerosis, caused bythickening artery walls and plaque formation. Biomechanical and/orhemodynamic forces, may affect or indicate the pathogenesis of coronaryatherosclerosis. For purposes of the disclosure, biomechanical and/orhemodynamic characteristics, forces, or parameters may include, but arenot limited to, the traction, traction force, pressure, pressuregradient, wall shear stress, axial plaque stress, radius gradient,and/or flow fractional reserve (FFR). In particular, wall shear stressmay affect the progression of coronary plaques, while axial plaquestress (APS), which may be the axial component of traction, mayinfluence the risk of plaque rupture. Axial plaque stress may correlateto radius gradient in a patient's vascular geometry. Radius gradient mayincorporate clinically relevant geometric parameters, including lesionlength, minimum lumen area, and stenosis severity. Since certainhemodynamic forces (e.g. wall shear stress, axial plaque stress, radiusgradient, etc.) may have unique characteristics in lesions as comparedto traditional metrics to characterize blood flow, e.g., lesion severityor fractional flow reserve (FFR), the consideration of certainhemodynamic forces, including, but not limited to, the wall shearstress, axial plaque stress, and radius gradient, in the clinicaldecision-making process may improve the risk stratification of plaquesand ultimately help patient care.

The embodiments of the present disclosure may provide a patient-specificevaluation of axial plaque stress and radius gradient to identifylesions or plaques exposed to high hemodynamic forces, using invasiveand noninvasive imaging methods. Such identification may provideimproved treatment strategies for vascular disease. In certainembodiments, the disclosed system and method may provide an evaluationof axial plaque stress and radius gradient to show why plaque rupturemay occur in a downstream segment of a vasculature as well as anupstream segment of a vasculature. Analyzing axial plaque stress withradius gradient may further show why plaques may be more likely torupture in short focal lesions rather than diffuse ones.

Furthermore, embodiments of the present disclosure may provide systemsand methods of monitoring hemodynamic forces (e.g., axial plaque stress,radius gradient, etc.) for discharged outpatients through mobile devicessuch as a smart-phone or smart-watch in order to provide continuedpersonalized care.

Referring now to the figures, FIG. 1 depicts a block diagram of anexemplary system 100 and network for estimating values of hemodynamicforces acting on plaque and monitoring patient risk, according to anexemplary embodiment. Specifically, FIG. 1 depicts a plurality ofphysicians 102 and third party providers 104, any of whom may beconnected to an electronic network 101, such as the Internet, throughone or more computers, servers, and/or handheld mobile devices.Physicians 102 and/or third party providers 104 may create or otherwiseobtain images of one or more patients' anatomy. For purposes of thedisclosure, a “patient” may refer to any individual or person for whomdiagnosis or treatment analysis is being performed, hemodynamic forcesare being estimated, or risks associated with hemodynamiccharacteristics are being monitored, or any individual or personassociated with the diagnosis or treatment of cardiovascular diseases orconditions, or any individual or person associated with the analysis ofhemodynamic characteristics of one or more individuals. The physicians102 and/or third party providers 104 may also obtain any combination ofpatient-specific parameters, including patient characteristics (e.g.,age, medical history, etc.) and physiological characteristics (e.g.,blood pressure, blood viscosity, patient activity or exercise level,etc.). Physicians 102 and/or third party providers 104 may transmit theanatomical images and/or patient-specific parameters to server systems106 over the electronic network 101. Server systems 106 may includestorage devices for storing images and data received from physicians 102and/or third party providers 104. Server systems 106 may also includeprocessing devices for processing images and data stored in the storagedevices.

FIG. 2A depicts pictorial and graphical diagrams of hemodynamic forcesacting on plaque, according to an exemplary embodiment. Specifically,FIG. 2A depicts a longitudinal section of vessel 202A, with a portion ofthe length of the vessel being afflicted by an obstruction 208A, andgraphs indicating fluctuations in stress values 204A and traction values206A along the length vessel 202A. The obstructive area 208A of thevessel may be caused by a plaque and/or lesion. The traction may bedefined as the total force per area acting on plaques or luminalsurfaces. As depicted in the longitudinal section of a vessel 202A, theaxial plaque stress (APS) may be defined as a projection of tractiononto the centerline of a vessel. Wall shear stress (WSS) may be definedas the tangential component of traction. As depicted in 204A, a changein axial plaque stress and, to a lesser degree, a change in the wallshear stress, may occur near the obstructive area 208A, characterizingan elevation of hemodynamic stress near a plaque or lesion. As depictedin 206A, the traction, and fractional flow reserve may decrease along avessel length, around and/or downstream from an obstructive area thatmay be caused by a plaque or lesion. Thus, hemodynamic characteristics(e.g., axial plaque stress) may uniquely characterize obstructivesegments of vessels and the present disclosure may be helpful inassessing the future risk of plaque rupture and/or to determinetreatment strategy for patients with coronary artery disease.

FIG. 2B depicts graphical diagrams illustrating the relationship betweenhemodynamic forces acting on plaque, according to an exemplaryembodiment of the present disclosure. Specifically, FIG. 2B depicts alongitudinal section of a vessel 202B, with a portion of the length ofthe vessel being afflicted by an obstruction 208B, a graphs depictingmethods for computing an approximated or analytic values of the radiusgradient (RG), 204B and 206B, respectively, with radius gradient (RG)values to be used in the computation of the axial plaque stress value.In one embodiment, an approximated value of the radius gradient, RG, maybe computed as follows:

${{RG} = \frac{r_{1} - r_{0}}{l}},$

where r₁ is the maximum radius and r₂ is the minimum radius over avessel of length I, as depicted in 204B. An analytic value of the radiusgradient, analytic RG, may be computed as follows:

${{{analytic}\mspace{14mu} {RG}} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}\frac{\Delta \; r_{i}}{\Delta \; s_{i}}}}},$

where N is the number of intervals over length, I of a vessel, Δr_(i) isthe change in radius over a change in interval, ΔS_(i), as depicted in206B.

The obstructive area 208B of the vessel may be caused by a plaque and/orlesion. The axial plaque stress (APS), which may be defined as theprojection of traction onto the centerline of a vessel, may be computedby multiplying the pressure times the radius gradient, with the radiusgradient being the luminal radius change over the length of a vesseland/or vessel segment. For example, an axial plaque stress upstream ofthe obstruction, {right arrow over (APS)}_(upstream), may be computed asfollows:

${\begin{matrix}{{\overset{\rightarrow}{APS}}_{upstream} = {{\sum{{\overset{\rightarrow}{T}}_{i}\sin \; \theta_{i}}} \approx {{Pressure}\frac{r_{1} - r_{0}}{\sqrt{l^{2} + \left( {r_{1} - r_{0}} \right)^{2}}}}}} \\{= {{{Pressure}\frac{\frac{r_{1} - r_{0}}{l}}{\sqrt{1 + \left( \frac{r_{1} - r_{0}}{l} \right)^{2}}}} \approx {{Pressure}\frac{r_{1} - r_{0}}{l}}}} \\{= {{{Pressure} \cdot {Radius}}\mspace{14mu} {Gradient}}}\end{matrix}{where}}\mspace{14mu} \underset{T_{i}}{\rightarrow}\mspace{14mu} {{is}\mspace{14mu} {the}}$

traction, r is the vessel radius, I is the length of the vessel underanalysis, and θ is the angle of the obstruction with respect to thecenterline of the vessel, as depicted in 202B.

FIG. 3 depicts a general embodiment of a method 300 for estimatinghemodynamic forces acting on plaque and monitoring patient risk. FIGS.4, 7-9, and 12-13 depict exemplary embodiments of method 300. Forexample, FIG. 4 depicts an embodiment of a process for estimating valuesof hemodynamic forces using non-invasive imaging and computational fluiddynamics to obtain hemodynamic characteristics. FIGS. 7-9 depictembodiments of estimating values of hemodynamic forces using a machinelearning algorithm. FIGS. 12-13 depict embodiments of estimating themaximum allowable values of hemodynamic forces and using the estimationsto monitor patient risk. FIGS. 5, 6, 8, and 11A-11B depict exemplarysteps for method 300 in FIG. 3. For example, FIG. 5 depicts anembodiment for performing step 302 of acquiring a patient-specificgeometric model non-invasively (e.g., cCTA). FIG. 6 depicts anembodiment for performing step 306 of outputting the estimated values ofhemodynamic characteristics (e.g., APS, WSS, etc.) using computationalfluid dynamics. FIG. 8 depicts another embodiment for performing step306, outputting estimated values of hemodynamic characteristics (e.g.,APS, WSS, etc.) using a machine learning algorithm. FIGS. 11A-11B depictan embodiment for performing step 308 of making appropriate clinicaldecisions based on the saved hemodynamic characteristics.

FIG. 3 is a block diagram of an exemplary method 300 of estimatinghemodynamic forces acting on plaque and monitoring patient risk,according to an exemplary embodiment. The method of FIG. 3 may beperformed by server systems 106, based on information, images, and datareceived from physicians 102 and/or third party providers 104 overelectronic network 101.

In one embodiment, step 302 may include acquiring a patient-specificgeometric model in an electronic storage medium of the server systems106. Specifically, receiving the patient-specific geometric model mayinclude either generating the patient-specific geometric model at theserver system 106, or receiving one over an electronic network (e.g.,electronic network 101). In one embodiment, the geometric model may bederived from images of the person acquired invasively or non-invasivelyvia one or more available imaging or scanning modalities. Non-invasivemethods for generating the geometric model may include performingcardiac CT imaging of the patient. Invasive methods for generating thegeometric model may include performing intravascular ultrasound (IVUS)imaging or optical coherence tomography (OCT) of the target vasculature.The invasively and/or non-invasively acquired image may then besegmented manually or automatically to identify voxels belonging to thevessels and/or lumen of interest. Once the voxels are identified, ageometric model may be derived (e.g., using marching cubes). In oneembodiment, the patient-specific geometric model may include acardiovascular model of a specific person and/or a patient's ascendingaorta and coronary artery tree. In another embodiment, thepatient-specific geometric model may be of a vascular model other thanthe cardiovascular model. In one embodiment, the geometric model may berepresented as a list of points in space (possibly with a list ofneighbors for each point) in which the space may be mapped to spatialunits between points (e.g., millimeters).

In one embodiment, step 304 may include measuring, deriving, orobtaining one or more patient-specific parameters invasively ornon-invasively in an electronic storage medium of the server systems106. For purposes of the disclosure, these patient-specific parametersmay include, but are not limited to, patient characteristics (e.g., age,gender, etc.), physiological characteristics (e.g., hematocrit level,blood pressure, heart rate, etc.), geometric characteristics (e.g.,radius gradient, lumen characteristics, stenosis characteristics, etc.),plaque characteristics (e.g., location of plaque, adverse plaquecharacteristics score, plaque burden, presence of napkin ring, intensityof plaque, type of plaque, etc.), simplified hemodynamic characteristics(e.g., wall shear stress and axial plaque stress values derived fromcomputational fluid dynamics), and/or coronary dynamics characteristics(e.g., distensibility of coronary artery over cardiac cycle, bifurcationangle change over cardiac cycle, curvature change over cardiac cycle,etc.).

In one embodiment, measuring or deriving patient-specific parameters mayalso include computing simplified hemodynamics characteristics. In oneembodiment, the simplified hemodynamics characteristics (e.g., wallshear stress, axial plaque stress, etc.) may be derived fromHagen-Poiseuille flow assumptions.

Any of the above-mentioned patient-specific parameters (e.g., patientcharacteristics, physiological characteristics, geometriccharacteristics, plaque characteristics, simplified hemodynamiccharacteristics, and/or coronary dynamics characteristics) may be usedto measure or derive other patient-specific parameters. In oneembodiment, the patient-specific parameters may be used as featurevectors to train and apply machine learning algorithm (e.g., as in step306).

In one embodiment, step 306 may include determining biophysical and/orhemodynamic characteristics (e.g., axial plaque stress, wall shearstress, etc.) using computational fluid dynamics and/or a machinelearning algorithm. In one embodiment, the simplified hemodynamicscharacteristics (e.g., wall shear stress, axial plaque stress, etc.) maybe derived from Hagen-Poiseuille flow assumptions. For example, the wallshear stress may be derived by computing the cross-sectional area at apoint i (A_(i)) of the patient's vasculature, computing the effectivelumen diameter (D_(i)), where

${D_{i} = {2\sqrt{\frac{A_{i}}{\pi}}}},$

and estimating the wall shear stress at the point i (WSS_(i)) using apressure gradient (PG_(i)) computed from a flow simulation ormeasurements, where

${D_{i} = {2\sqrt{\frac{A_{i}}{\pi}}}},$

In another example, the axial plaque stress may be derived by computingthe radius gradient at a point i (RG_(i)) over an interval (ds), where

${{RG}_{i} = {\left( {\sqrt{\frac{A_{i + 1}}{\pi}} - \sqrt{\frac{A_{i}}{\pi}}} \right)/{s}}},$

and estimating APS (APS_(i)) using a radius gradient (RG_(i)) computedfrom flow simulation or measurements (e.g., as in 206B and 208B of FIG.2B), where

${APS}_{i} = {{{RG}_{analytic} \cdot {Pressure}} = {{\frac{1}{N}{\sum\limits_{1}^{N}{{{RG}_{i} \cdot {Pressure}}\mspace{14mu} {and}\mspace{14mu} {APS}_{i}}}} = {{RG}_{ave} \cdot {{Pressure}.}}}}$

In one embodiment, the simplified hemodynamic characteristics may beused to compute more accurate hemodynamic characteristics and/or be usedas part of a machine learning algorithm to obtain the hemodynamiccharacteristics for points on the geometric model where the simplifiedhemodynamic characteristics may not be known.

In one embodiment, step 306 may include using the patient-specificparameters obtained from step 304 (e.g., patient characteristics,physiological characteristics, geometric characteristics, plaquecharacteristics, simplified hemodynamic characteristics, and/or coronarydynamics characteristics) to form feature vectors to train and apply amachine learning algorithm to determine biomechanical and/or hemodynamiccharacteristics. For example, for one or more points on the geometricmodel where simplified hemodynamic characteristics can be calculatedusing computational fluid dynamics, a feature vector may then beassociated with the computed hemodynamic characteristics for the one ormore points on the geometric model. The feature vectors and theirassociated biomechanical and/or hemodynamic characteristics may be usedto train a machine learning algorithm that may be stored in anelectronic storage medium. The trained machine learning algorithm may beapplied to another geometric model using another set of patient-specificparameters to derive biomechanical and/or hemodynamic characteristicsfor points on the geometric model.

In one embodiment, step 308 may include outputting the estimates ofbiomechanical and/or hemodynamic characteristics (e.g., wall shearstress, axial plaque stress, radius gradient, etc.) to an electronicstorage and/or to a display screen. The estimates of the biomechanicaland/or hemodynamic characteristics may be displayed in greyscale orcolor in 2D or 3D. The estimates of the biophysical and/or hemodynamiccharacteristics may be overlaid on the geometric model and/or overlaidon an image of the vasculature of interest. For purposes of disclosure,an “electronic storage medium” may include, but is not limited to, ahard drive, network drive, cloud drive, mobile phone, tablet, or thelike, whether or not affixed to a display screen.

In one embodiment, step 310 may include making an appropriate clinicaldecision based on the output biophysical and/or hemodynamic results. Inone embodiment, biomechanical and/or hemodynamic characteristicsobtained under a given patient physiological state (e.g., rest,hyperemia, varied levels of stress, etc.) may be used to detect abnormalhemodynamic characteristics. In another embodiment, abnormal levels ofbiomechanical and/or hemodynamic characteristics may activate a warningsignal that may be generated from a mobile device to notify patientsand/or physicians. In another embodiment, the one or morepatient-specific parameters and outputted biomechanical and/orhemodynamic characteristics may be used to compute a risk score, where

${{Risk}\mspace{14mu} {score}} = {{f\left( \frac{{Stress}\mspace{14mu} {within}\mspace{14mu} {the}\mspace{14mu} {plaque}}{{Ultimate}\mspace{14mu} {Strength}\mspace{14mu} {of}\mspace{14mu} {Plaque}} \right)} \approx {{g\left( {{APS},{APCscore},{etc}} \right)}.}}$

In yet another embodiment, a cumulative history of biomechanical and/orhemodynamic results may be used to make the appropriate clinicaldecisions.

FIG. 4 is a block diagram of an exemplary method of estimatinghemodynamic forces acting on plaque and monitoring risk, usingnon-invasive imaging and computational fluid dynamics to estimatehemodynamic characteristics, according to an exemplary embodiment of thepresent disclosure. The method of FIG. 4 may be performed by serversystems 106, based on information, images, and data received fromphysicians 102 and/or third party providers 104 over electronic network101.

In one embodiment, step 402 may include acquiring a patient-specificgeometric model non-invasively (e.g., by coronary computerizedtomography). This geometrical model may be represented as a list ofpoints in space (possibly with a list of neighbors for each point) inwhich the space may be mapped to spatial units between points (e.g.,millimeters). The geometric model may be generated by performing one ormore cardiac or coronary computerized tomography (cCT) imaging of thepatient. The one or more cCT images may be segmented manually orautomatically to identify voxels belonging to the aorta and the lumen ofthe coronary arteries. Once the voxels are identified, the geometricmodel may be derived (e.g., using marching cubes). In one embodiment,the patient-specific geometric model may include a cardiovascular modelof a specific person and/or a patient's ascending aorta and coronaryartery tree. In another embodiment, the patient-specific geometric modelmay be of a vascular model other than the cardiovascular model.

In one embodiment, step 404 may include measuring or derivingpatient-specific parameters non-invasively (e.g., by using computationalfluid dynamics). The measured or derived patient-specific parameters maybe stored in an electronic storage medium. These patient-specificparameters may include, but are not limited to patient characteristics(e.g., age, gender, etc.), physiological characteristics (e.g.,hematocrit level, blood pressure, heart rate, etc.), geometriccharacteristics (e.g., radius gradient, lumen characteristics, stenosischaracteristics, etc.), plaque characteristics (e.g., location ofplaque, adverse plaque characteristics score, plaque burden, presence ofnapkin ring, intensity of plaque, type of plaque, etc.), simplifiedhemodynamic characteristics (e.g., wall shear stress and axial plaquestress values derived from computational fluid dynamics), and/orcoronary dynamics characteristics (e.g., distensibility of coronaryartery over cardiac cycle, bifurcation angle change over cardiac cycle,curvature change over cardiac cycle, etc.). Any of the above-mentionedpatient-specific parameters may be used to measure or derive otherpatient-specific parameters.

Steps 406A, 406B, 406C, 406D, and 406E depict the measured or derivedpatient characteristics, physiological characteristics, geometriccharacteristics, plaque characteristics, and coronary dynamicscharacteristics, respectively. The patient-specific parameters may bestored in an electronic storage medium.

The patient characteristics 406A may include a patient's age, gender,weight, or any other biographical information that may be relevant forthe computation of hemodynamic characteristics.

In one embodiment, measuring or deriving physiological characteristics406B may include, but is not limited to, obtaining a blood pressureprofile, EKG, a measurement of heart rate or heart rate change, apressure gradient along a vessel centerline, and/or blood contentprofile (e.g., hematocrit level). A pressure gradient may be derivedfrom a simulation or computed over a strip sliced along the vesselcenterline (e.g., a 1 mm interval).

In one embodiment, measuring or deriving geometric characteristics 406Cmay include measuring or deriving lumen characteristics, lesioncharacteristics, stenosis characteristics, and characteristics of thecoronary centerline. The lumen characteristics may include the lumendiameter, the ratio of lumen cross-sectional area with respect to themain ostia (left main or right coronary artery), the degree of taperingin cross-sectional lumen area along the centerline, where centerlinepoints within a certain interval (e.g., twice the diameter of thevessel) may be sampled and a slope of linearly-fitted cross-sectionalarea may be computed, the irregularity (or circularity) ofcross-sectional lumen boundary, characteristics of coronary lumenintensity at a lesion, where the characteristics may include intensitychange along the centerline (e.g., using the slope of a linearly fittedintensity variation), the characteristics of surface of coronarygeometry at a lesion (e.g., Gaussian maximum, minimum, mean, etc.), andthe radius gradient (e.g., by measuring the radius change from thestarting or ending point of a lesion point to minimum lumen arealocation divided by lesion length). The ratio of lumen cross-sectionalarea with respect to the main ostia (e.g., left main or right coronaryartery) may be obtained by measuring the cross-sectional area at theleft main ostium, normalizing the cross-sectional area of the leftcoronary using the left main ostium cross-sectional area, measuring thecross-sectional area at the right coronary artery ostium, andnormalizing the cross-sectional area of the right coronary using a rightcoronary artery ostium area. Stenotic and lesion characteristics mayinclude the degree of stenosis (e.g., by using a Fourier smoothed areagraph or kernel regression), the length of a stenotic lesions (e.g., bycomputing the proximal and distal locations from the stenotic lesionwhere cross-sectional area is determined), and location of a stenoticlesion (e.g., the distance from stenotic lesion to the main ostia).Characteristics of the coronary centerline (e.g., topology) may includethe curvature and tortuosity (non-planarity) of the coronary centerline.The curvature may be obtained by computing the Frenet curvature, κ,where

$\kappa = \frac{{p^{\prime} \times p^{''}}}{{p^{\prime}}^{3}}$

and ρ may be a coordinate of centerline parameterized by cumulativearc-length to the starting point, and by computing an inverse of theradius of a circumscribed circle along the centerline points. Thetortuosity may be obtained by computing the Frenet torsion, τ, where

${\tau = \frac{\left( {p^{\prime} \times p^{''}} \right) \cdot p^{\prime\prime\prime}}{{{p^{\prime} \times p^{''}}}^{2}}},$

and where ρ may be a coordinate of a centerline. In one embodiment,measuring or deriving the geometric characteristics 406C may alsoinclude obtaining the mass of a myocardium or tissue of interest.

In one embodiment, measuring or deriving plaque characteristics 406D mayinclude obtaining the location of plaque, an adverse plaquecharacteristics score, the plaque burden (e.g., cap thickness, wallthickness, area, volume, etc.), information on the existence orcharacteristics of a napkin ring, plaque intensity, and/or plaque type(e.g., calcified, non-calcified, etc.). The location of a plaque mayinclude, but is not limited to, the distance from the plaque to theclosest upstream bifurcation point, the angle of bifurcation of thecoronary branches if the plaque is located at the bifurcation, thedistance from the plaque location to an ostium (left main or rightcoronary artery), and/or the distance from the plaque location to thenearest downstream and/or upstream bifurcation.

In one embodiment, measuring or deriving coronary dynamicscharacteristics 406E may include obtaining the distensibility of acoronary artery over a cardiac cycle, the change in a bifurcation angleover a cardiac cycle, and/or the change in curvature of a vessel over acardiac cycle. The coronary dynamics characteristics may be derived froma multi-phase coronary CT angiography (e.g., diastole and systole).

In one embodiment, step 408 may include outputting hemodynamiccharacteristics (e.g., axial plaque stress, wall shear stress, etc.)using computational fluid dynamics. In one embodiment, the simplifiedhemodynamics characteristics (e.g., wall shear stress, axial plaquestress, etc.) may be derived from Hagen-Poiseuille flow assumptions. Forexample, the wall shear stress may be derived by computing thecross-sectional area at a point i (A_(i)) on a vasculature, computingthe effective lumen diameter (D_(i)), where

${D_{i} = {2\sqrt{\frac{A_{i}}{\pi}}}},$

and estimating the wall shear stress at the point i (WSS_(i)) using apressure gradient (PG_(i)) computed from a flow simulation ormeasurements, where

${WSS}_{i} = {{PG}_{i} \cdot {\frac{D_{i}}{4}.}}$

In another example, the axial plaque stress may be derived by computingthe radius gradient at a point i (RG_(i)) over an interval (ds), where

${{RG}_{i} = {\left( {\sqrt{\frac{A_{i + 1}}{\pi}} - \sqrt{\frac{A_{i}}{\pi}}} \right)/{s}}},$

and estimating the axial plaque stress over a point i, APS_(i), using aradius gradient (RG_(i)) computed from flow simulation or measurements(e.g., as in 206B and 208B of FIG. 2B), where

${APS}_{i} = {{{RG}_{analytic} \cdot {Pressure}} = {{\frac{1}{N}{\sum\limits_{1}^{N}{{{RG}_{i} \cdot {Pressure}}\mspace{14mu} {and}\mspace{14mu} {APS}_{i}}}} = {{RG}_{ave} \cdot {{Pressure}.}}}}$

In one embodiment, step 408 may also include outputting the estimates ofhemodynamic characteristics to an electronic storage medium (e.g., harddisk, network drive, portable disk, smart phone, tablet etc.) and/or toa display screen. The estimates of the output hemodynamiccharacteristics may be displayed in greyscale or color in 2D or 3D. Theestimates of the hemodynamic characteristics may be overlaid on thegeometric model and/or overlaid on an image of the vasculature ofinterest.

In one embodiment, step 410 may include making the appropriate clinicaldecision based on the outputted hemodynamic results. In one embodiment,hemodynamic characteristics obtained under a given patient physiologicalstate (e.g., rest, hyperemia, varied levels of stress, etc.) may be usedto detect abnormal hemodynamic characteristics. In another embodiment,abnormal levels of hemodynamic characteristics may activate a warningsignal that may be generated from a mobile device to notify patientsand/or physicians. In another embodiment, the one or morepatient-specific parameters and outputted hemodynamic characteristicsmay be used compute a risk score, where

${{Risk}\mspace{14mu} {score}} = {{f\left( \frac{{Stress}\mspace{14mu} {within}\mspace{14mu} {the}\mspace{14mu} {plaque}}{{Ultimate}\mspace{14mu} {Strength}\mspace{14mu} {of}\mspace{14mu} {Plaque}} \right)} \approx {{g\left( {{APS},{APCscore},{etc}} \right)}.}}$

In yet another embodiment, a cumulative history of biomechanical and/orhemodynamic results may be used to make the appropriate clinicaldecisions.

FIG. 5 depicts an exemplary method 500 of acquiring a patient-specificgeometric model non-invasively (e.g., through coronary computerizedtomography angiography (cCTA)), according to an exemplary embodiment ofthe present disclosure. FIG. 5 may include an exemplary method ofperforming step 302 of method 300 in FIG. 3, step 402 of method 400 inFIG. 4, and/or the step of non-invasively acquiring a patient-specificgeometric model for any one of the embodiments of the present disclosurethat includes such a step.

In one embodiment, step 502 may include performing a cardiac CT imagingof a patient in the end diastole phase of a cardiac cycle. In anotherembodiment, step 502 may include obtaining one or more images of apatient using a non-invasive scanning modality other than a computerizedtomography. In another embodiment, step 502 may include obtaining one ormore images of a patient during a phase of a cardiac cycle other thanthe end diastole phase.

In one embodiment, step 504 may include segmenting the one or morecardiac CT images manually or automatically into one or more voxels. Inone embodiment, step 506 may include identifying the voxels belonging tothe vasculature of interest (e.g., aorta and lumen of the coronaryarteries). The segmentation and/or identification may be performed usinga processor.

In one embodiment, step 508 may include deriving the patient-specificgeometric model from the identified voxels (e.g., using marching cubes).In one embodiment step 508 may also include updating the geometric modelbased on one or more measured or derived patient-specific parameters, orone or more measured or derived biomechanical and/or hemodynamiccharacteristics. In one embodiment, step 508 may also include updatingthe geometric model based on an invasively acquired images of a patient.

FIG. 6 depicts an exemplary method 600 of using patient-specificparameters to output hemodynamic characteristics, using invasive (e.g.,IVUS, OCT, motorized pull-back mechanism, etc.) and/or non-invasive(e.g., computational fluid dynamics) measurements, according to anexemplary embodiment of the present disclosure. FIG. 6 may include anexemplary method of performing step 306 of method 300 in FIG. 3 and/orstep 408 of method 400 in FIG. 4.

In one embodiment, step 602 may include computing a maximum pressure ofa patient from a pulsatile blood pressure. In another embodiment, step602 may include obtaining the maximum pressure without taking thepulsatile blood pressure of a patient. Step 604 may include computingthe pressure change during a cardiac cycle using the maximum pressureobtained in step 602.

In one embodiment, step 606 may include computing the pressure gradientusing flow simulation measurements of the pressure change obtained instep 602. For example, a pressure gradient may be computed by utilizingspatial information along a pull-back path using the pressure change. Inanother embodiment, step 606 may include obtaining the pressure gradientwithout computing the maximum pressure or pressure change in steps 602and 604, respectively.

Step 608 may include estimating the wall shear stress (WSS_(i)) usingthe pressure gradient (PG_(i)) and lumen diameter (D_(i)), where

${WSS}_{i} = {{PG}_{i} \cdot {\frac{D_{i}}{4}.}}$

In one embodiment, other hemodynamic characteristics (e.g., traction)may be computed using the pressure gradient, and lumen characteristics.

In one embodiment, step 610 may include obtaining the radius gradient(RG_(i)) from flow simulations or measurement. The flow simulations ormeasurements may occur invasively (e.g., using a pull-back path, OCT,IVUS, etc.) or non-invasively (e.g., using cCTA produced images). In oneembodiment, the radius gradient may be computed by using 3D geometryconstructed from optical coherence tomography or intravascularultrasound images co-registered to a bi-planar angiogram. In oneembodiment, the radius gradient (RG_(i)) may be approximated usingradius lengths, r₁ and r₂, and a lumen length, I, whereRG_(i)=(r₁−r₂)/I. In another embodiment, the radius gradient may becomputed at a point i (RG_(i)) over interval (ds) for a lumen with acircular area of A_(i), where

${RG}_{i} = {\left( {\sqrt{\frac{A_{i + 1}}{\pi}} - \sqrt{\frac{A_{i}}{\pi}}} \right)/{{s}.}}$

In one embodiment, step 612 may include estimating the axial plaquestress value at point i (APS_(i)) using pressure and radius gradient atpoint i (RG)_(i), where APS_(i)=RG_(i)* Pressure. The pressure may beobtained from computations of the pressure gradient in step 606. In oneembodiment, other hemodynamic characteristics (e.g., fractional flowreserve) may be computed using the pressure gradient, lumencharacteristics, and/or radius gradient.

Step 614 may include outputting the hemodynamic characteristics (e.g.,wall shear stress and axial plaque stress) onto an electronic storagemedium (e.g., hard disk, network drive, portable disk, smart phone,tablet etc.) and/or to a display screen. The estimates of the outputhemodynamic characteristics may be displayed in greyscale or color in 2Dor 3D. The estimates of the hemodynamic characteristics may be overlaidon the geometric model and/or overlaid on an image of the vasculature ofinterest.

FIGS. 7, 8, and 9 depict exemplary methods of estimating hemodynamicforces acting on plaque and monitoring risk, using a machine learningalgorithm to estimate hemodynamic characteristics, according to anexemplary embodiment of the present disclosure. Moreover, FIG. 7 mayinclude an exemplary method for training a machine learning algorithmfor estimating hemodynamic forces, using non-invasive imaging andcomputational fluid dynamics. The method depicted in FIG. 7 may be usedto train a machine learning algorithm that may be applied in the methodsdepicted in FIG. 8 or 9. While FIG. 8 may include an exemplary method ofapplying the trained machine learning algorithm using a non-invasivelyacquired geometric model of a target patient, FIG. 9 may include anexemplary method of applying a trained machine learning algorithm, usingan invasively acquired geometric model of a target patient.

FIG. 7 depicts an exemplary method 700 for training a machine learningalgorithm for estimating hemodynamic forces, using non-invasive imagingand computational fluid dynamics. In another embodiment, thepatient-specific geometric model may be acquired invasively (e.g.,through IVUS, OCT, pull-back, pressure wire, etc.), for the purposes oftraining a machine learning algorithm. In yet another embodiment, step702 may include receiving a database of geometric models from aplurality of patients for the purpose of training a machine learningalgorithm. The acquired geometric model may be represented as a list ofpoints in space (possibly with a list of neighbors for each point) inwhich the space may be mapped to spatial units between points (e.g.,millimeters). The acquired geometric model may be generated byperforming one or more cardiac or coronary computerized tomography (cCT)imaging of the patient. The one or more cCT images may be segmentedmanually or automatically to identify voxels belonging to the aorta andthe lumen of the coronary arteries. Once the voxels are identified, thegeometric model may be derived (e.g., using marching cubes). In oneembodiment, the patient-specific geometric model may include acardiovascular model of a specific person and/or a patient's ascendingaorta and coronary artery tree. In another embodiment, thepatient-specific geometric model may be of a vascular model other thanthe cardiovascular model.

In one embodiment, step 704 may include measuring, deriving, orobtaining patient-specific parameters non-invasively using computationalfluid dynamics (CFD). The measured or derived patient-specificparameters may be stored in an electronic storage medium. In oneembodiment, the patient-specific parameters may be obtained from aplurality of patients and/or their database of geometric models, for thepurpose of training a machine learning algorithm. These patient-specificparameters may include, but are not limited to patient characteristics(e.g., age, gender, etc.), physiological characteristics (e.g.,hematocrit level, blood pressure, heart rate, etc.), geometriccharacteristics (e.g., radius gradient, lumen characteristics, stenosischaracteristics, etc.), plaque characteristics (e.g., location ofplaque, adverse plaque characteristics score, plaque burden, presence ofnapkin ring, intensity of plaque, type of plaque, etc.), simplifiedhemodynamic characteristics (e.g., wall shear stress and axial plaquestress values derived from computational fluid dynamics), and/orcoronary dynamics characteristics (e.g., distensibility of coronaryartery over cardiac cycle, bifurcation angle change over cardiac cycle,curvature change over cardiac cycle, etc.). Any of the above-mentionedpatient-specific parameters may be used to measure or derive otherpatient-specific parameters. In one embodiment, step 704 may beperformed by a processor.

Steps 706A, 706B, 706C, 706D, and 706E depict the measured or derivedpatient characteristics, physiological characteristics, geometriccharacteristics, plaque characteristics, and coronary dynamicscharacteristics, respectively. The patient-specific parameters may bestored in an electronic storage medium.

In one embodiment, step 708 may include outputting one or more simulatedhemodynamic characteristics (e.g., axial plaque stress, wall shearstress, etc.), using computational fluid dynamics, for one or morepoints on the acquired geometric model. In one embodiment, step 708 maybe performed by using processors of server systems 106. Step 708 may beperformed using the method depicted in FIG. 6.

In one embodiment, step 710 may include associating feature vectors,comprising the measured, derived, or obtained patient-specificparameters, with their corresponding hemodynamic characteristics (e.g.,axial plaque stress, wall shear stress, etc.), for one or more points onthe geometric model. In one embodiment, step 710 may be performed byusing processors of server systems 106.

In one embodiment, step 712 may include using the feature vectors andtheir associated hemodynamic characteristics to train a machine learningalgorithm to predict hemodynamic characteristics. In one embodiment, thefeature vectors may be obtained from step 710. The machine learningalgorithm may take many forms, including, but not limited to, amulti-layer perceptron, deep learning, support vector machines, randomforests, k-nearest neighbors, Bayes networks, etc. Step 712 may beperformed using processing devices of server systems 106.

In one embodiment, step 714 may include outputting the trained machinelearning algorithm, including feature weights, into an electronicstorage medium of server systems 106. The stored feature weights maydefine the extent to which patient-specific parameters are predictive ofhemodynamic characteristics.

FIG. 8 depicts an exemplary method 800 of applying a trained machinelearning algorithm to predict hemodynamic characteristics using anon-invasively acquired geometric model of a target patient. The trainedmachine learning algorithm may be that obtained from method 700 of FIG.7.

In one embodiment, step 802 may include acquiring a patient-specificgeometric model non-invasively (e.g., through coronary computerizedtomography angiography). The acquired geometric model may be of thepatient for which the hemodynamic characteristics are to be estimated byapplying a trained machine learning algorithm. The acquired geometricalmodel may be represented as a list of points in space (possibly with alist of neighbors for each point) in which the space may be mapped tospatial units between points (e.g., millimeters). The acquired geometricmodel may be generated by performing one or more cardiac or coronarycomputerized tomography (cCT) imaging of the patient. The one or morecCT images may be segmented manually or automatically to identify voxelsbelonging to the aorta and the lumen of the coronary arteries. Once thevoxels are identified, the geometric model may be derived (e.g., usingmarching cubes). In one embodiment, the patient-specific geometric modelmay include a cardiovascular model of a specific person and/or apatient's ascending aorta and coronary artery tree. In anotherembodiment, the patient-specific geometric model may be of a vascularmodel other than the cardiovascular model. The acquired geometric modelmay be stored in an electronic storage medium of server systems 106.

In one embodiment, step 804 may include measuring, deriving, orobtaining patient-specific parameters non-invasively using computationalfluid dynamics (CFD). The measured or derived patient-specificparameters may be stored in an electronic storage medium. Thepatient-specific parameters may be obtained from the patient for whomthe hemodynamic characteristics and/or risk analysis is being sought, orfrom the patient's geometric model. These patient-specific parametersmay include, but are not limited to patient characteristics (e.g., age,gender, etc.), physiological characteristics (e.g., hematocrit level,blood pressure, heart rate, etc.), geometric characteristics (e.g.,radius gradient, lumen characteristics, stenosis characteristics, etc.),plaque characteristics (e.g., location of plaque, adverse plaquecharacteristics score, plaque burden, presence of napkin ring, intensityof plaque, type of plaque, etc.), simplified hemodynamic characteristics(e.g., wall shear stress and axial plaque stress values derived fromcomputational fluid dynamics), and/or coronary dynamics characteristics(e.g., distensibility of coronary artery over cardiac cycle, bifurcationangle change over cardiac cycle, curvature change over cardiac cycle,etc.). Any of the above-mentioned patient-specific parameters may beused to measure or derive other patient-specific parameters. In oneembodiment, step 804 may be performed by a processor.

Steps 806A, 806B, 806C, 806D, and 806E depict the measured or derivedpatient characteristics, physiological characteristics, geometriccharacteristics, plaque characteristics, and coronary dynamicscharacteristics, respectively. The patient-specific parameters may bestored in an electronic storage medium.

In one embodiment, step 808 may include applying a trained machinelearning algorithm to predict hemodynamic characteristics (e.g., axialplaque stress, wall shear stress, etc.) for one or more points on thegeometric model. In one embodiment, step 808 may include using thetrained machine learning algorithm obtained from step 714 in method 700,as depicted in FIG. 7. In one embodiment, step 808 may include using thepatient-specific parameters obtained from step 804 for one or morepoints on the patient-specific geometric model when applying the trainedmachine learning algorithm to predict hemodynamic characteristics forthose points. The machine learning algorithm may take many forms,including, but not limited to, a multi-layer perceptron, multivariateregression, deep learning, support vector machines, random forests,k-nearest neighbors, Bayes networks, etc. Step 808 may use processingdevices of server systems 106.

In one embodiment, step 810 may include outputting the hemodynamiccharacteristics (e.g., axial plaque stress, wall shear stress, etc.)and/or results of the machine learning algorithm into an electronicstorage medium of server systems 106. The hemodynamic characteristicsmay be those obtained from the application of a trained machine learningalgorithm in step 808. In one embodiment, the output may includepatient-specific characteristics other than hemodynamic characteristics.In one embodiment, step 810 may further include monitoring the risk of apatient and/or assessing treatment strategies based on the output.

FIG. 9 may depict an exemplary method 900 of applying a trained machinelearning algorithm to predict hemodynamic characteristics using aninvasively acquired geometric model of a target patient. The trainedmachine learning algorithm may be that obtained from method 700 of FIG.7.

In one embodiment, step 902 may include acquiring a patient-specificgeometric model invasively (e.g., through an optical coherencetomography (OCT), intravascular ultrasound (IVUS), pressure wire, etc.).The acquired geometric model may be of the patient for which thehemodynamic characteristics are to be estimated by applying a trainedmachine learning algorithm. The acquired geometrical model may berepresented as a list of points in space (possibly with a list ofneighbors for each point) in which the space may be mapped to spatialunits between points (e.g., millimeters). Invasive methods forgenerating the geometric model may include obtaining one or more imagesby using a pressure wire or by performing intravascular ultrasound(IVUS) imaging or optical coherence tomography (OCT) of the targetvasculature. For straight geometries constructed from intravascularimaging, images may be bent or otherwise modified by applying acurvature computed from a co-registered angiogram. Applying thecurvature may include first computing the curvature of a vessel from anangiogram and co-registering the optical coherence tomography orintravascular ultrasound-images to the angiogram. The acquired image maythen be segmented manually or automatically to identify voxels belongingto the vessels and/or lumen of interest. The segmentation may beperformed by a processor. Once the voxels are identified, a geometricmodel may be derived (e.g., using marching cubes). In one embodiment,the patient-specific geometric model may include a cardiovascular modelof a specific person and/or a patient's ascending aorta and coronaryartery tree. In another embodiment, the patient-specific geometric modelmay be of a vascular model other than the cardiovascular model. Theacquired geometric model may be stored in an electronic storage mediumof server systems 106.

In one embodiment, step 904 may include measuring, deriving, orobtaining patient-specific parameters invasively (e.g., from opticalcoherence tomography, intravascular ultrasound, pressure-wire, etc.).The measured or derived patient-specific parameters may be stored in anelectronic storage medium. The patient-specific parameters may beobtained from the patient for whom the hemodynamic characteristicsand/or risk analysis is being sought, or from the patient's geometricmodel. These patient-specific parameters may include, but are notlimited to, patient characteristics (e.g., age, gender, etc.),physiological characteristics (e.g., hematocrit level, blood pressure,heart rate, etc.), geometric characteristics (e.g., radius gradient,lumen characteristics, stenosis characteristics, etc.), plaquecharacteristics (e.g., location of plaque, adverse plaquecharacteristics score, plaque burden, presence of napkin ring, intensityof plaque, type of plaque, etc.), simplified hemodynamic characteristics(e.g., wall shear stress and axial plaque stress values derived fromcomputational fluid dynamics), and/or coronary dynamics characteristics(e.g., distensibility of coronary artery over cardiac cycle, bifurcationangle change over cardiac cycle, curvature change over cardiac cycle,etc.). Any of the above-mentioned patient-specific parameters may beused to measure or derive other patient-specific parameters. In oneembodiment, step 904 may be performed by a processor.

Steps 906A, 906B, 906C, 906D, and 906E depict the measured, derived, orobtained patient characteristics, physiological characteristics,geometric characteristics, plaque characteristics, and coronary dynamicscharacteristics, respectively. The list of patient-specific parametersmay be the same as the list used in the training mode (e.g., as inmethod 700). The patient-specific parameters may be stored in anelectronic storage medium.

In one embodiment, the list of physiological characteristics 906B may bemeasured, derived, or obtained using a motorized pull-back system. Forexample, the pressure along the vessel length may be measured using apressure wire. The maximum pressure may be computed during a cardiaccycle. In one embodiment, the pressure gradient (PG_(i)) may be computedby using spatial information along one or more pull-back paths, where

${{PG}_{i} = \frac{\Delta \; P_{i}}{\Delta \; S_{i}}},$

with ΔP_(i) being a change in pressure and ΔS_(i) being a change inspatial metric. Furthermore, noise signals from pressure measurementsmay be reduced by using filtering techniques (e.g., Kalman filtering).

In one embodiment, the list of geometric characteristics 906C may bemeasured, derived, or obtained from optical coherence tomography or fromintravascular ultrasound images co-registered to an angiogram. Thesegeometric characteristics may include, but are not limited to, theradius gradient, the minimum lumen area and diameter, the degree ofstenosis at a lesion, the location of stenotic lesions, the length ofstenotic lesions, the irregularity (or circularity) of cross-sectionallumen boundaries, the characteristics of coronary lumen intensity at alesion, the characteristics of surface of coronary geometry at a lesion,and the characteristics of coronary centerline (e.g., topology) at oneor more lesions, etc. In one embodiment, the radius gradient, RG_(i),may be computed by utilizing 3D geometry constructed from opticalcoherence tomography or intravascular ultrasound images co-registered toan angiogram, using the formula,

${{RG}_{i} = \frac{\Delta \; R_{i}}{\Delta \; S_{i}}},$

where ΔR_(i) is the change in radius and ΔS_(i) is an increment ofvessel length. Likewise, the minimum lumen area and minimum lumendiameter may be computed from the radius gradient and/or from the 3Dgeometry constructed from optical coherence tomography or intravascularultrasound images co-registered to angiogram. The degree of stenosis ata lesion (e.g., percentage diameter/area stenosis) may be computed bydetermining the virtual reference area profile using Fourier smoothingor kernel regression. The percent stenosis of lesion may be computedusing the virtual reference area profile along the vessel centerline.The location of stenotic lesions may be obtained by computing thedistance (e.g., parametric arc length of centerline) from the mainostium to the start or center of the lesion. The length of stenoticlesions may be obtained by computing the proximal and distal locationsfrom the stenotic lesion where cross-sectional area may be determined.The characteristics of coronary lumen intensity at a lesion may includethe intensity change along the centerline, which may be computed, forexample, by using the slope of a linearly-fitted intensity variation.The characteristics of surface of coronary geometry at a lesion mayinclude the 3D surface curvature of geometry (e.g., Gaussian, maximum,minimum, mean, etc.). The characteristics of coronary centerline (e.g.,topology) at one or more lesions may include the curvature (bending) ofcoronary centerline and/or the tortuosity (non-planarity) of thecoronary centerline. The curvature (bending) of coronary centerline maybe obtained by computing the Frenet curvature, κ, in the formula

${\kappa = \frac{{p^{\prime} \times p^{''}}}{{p^{\prime}}^{3}}},$

where p may be a coordinate of centerline parameterized by cumulativearc-length to the starting point, and/or by computing an inverse of theradius of a circumscribed circle along the centerline points. Thetortuosity (non-planarity) of the coronary centerline may be obtained bycomputing the Frenet torsion, τ, in the formula,

${\tau = \frac{\left( {p^{\prime} \times p^{''}} \right) \cdot p^{\prime\prime\prime}}{{{p^{\prime} \times p^{''}}}^{2}}},$

where p may be a coordinate of a centerline.

In one embodiment, the plaque characteristics 906D may be measured,derived, or obtained using coronary CT angiography, intravascularultrasound, near-infrared spectroscopy, and/or optical coherencetomography. The plaque characteristics may include, but are not limitedto the location of plaque along the centerline of the vessel, the plaqueburden (e.g., cap thickness, wall thickness, area, volume, etc.), thepresence of a Napkin ring, the intensity of plaque, the type of plaque(e.g., calcified, non-calcified, etc.), the distance from the plaquelocation to the ostium, the distance from the plaque location to thenearest downstream or upstream bifurcation, and/or an adverse plaquecharacteristics (APC) score.

In one embodiment, the adverse plaque characteristics score (APC score)may be computed based on the presence of positive remodeling, presenceof a low attenuation plaque, and/or presence of spotty intra-plaquecalcification. Determining the presence of positive remodeling mayinclude determining a diseased segment based on the degree of stenosisor the presence of plaque in the wall segmentation. A positiveremodeling index may be computed by evaluating a cross-sectional area(CSA) of a vessel (EEM) at a lesion and reference segments based on thefollowing equation: positive remodeling

${index} = {\frac{{CSA}\mspace{14mu} {of}\mspace{14mu} {EEM}\mspace{14mu} {at}\mspace{14mu} {lesion}}{{CSA}\mspace{14mu} {of}\mspace{14mu} {EEM}\mspace{14mu} {at}\mspace{14mu} {reference}}.}$

If the positive remodeling index is greater than 1.05, the presence of apositive remodeling and/or the positive remodeling index may bereported. Determining the presence of low attenuation plaque may includedetecting non-calcified plaques in wall segmentation at a diseasedsegment. If a region of non-calcified plaque has an intensity of lessthan or equal to 30 Hounsfield Units (HU), the presence of lowattenuation plaque and/or the volume of non-calcified plaque may bereported. In some embodiments, the presence of low attenuation plaqueand/or the volume of non-calcified plaque may be reported even if aregion of non-calcified plaque has an intensity of less than or equal to50 Hounsfield Units (HU). Determining the presence of spotty and/orblob-shaped intra-plaque calcification may include detecting calcifiedplaques in wall segmentation at a diseased segment. A Hessian-basedeigenvalue analysis may be utilized to detect blob-shaped calcifiedplaques. If the diameter of intra-lesion nodular calcified plaque isless than 3 mm, the presence of spotty and/or blob-shaped calcificationand/or the diameter of the plaque may be reported.

In one embodiment, the coronary dynamics characteristics 906E may bemeasured, derived, or obtained from multi-phase coronary computedtomography angiography (e.g., diastole and systole) or derived from ananalysis of a cine-angiogram. The coronary dynamics characteristics mayinclude, but are not limited to, the distensibility of a coronary arteryover the cardiac cycle, the bifurcation angle change over the cardiaccycle, and/or the curvature change over the cardiac cycle.

In one embodiment, step 908 may include applying a trained machinelearning algorithm to predict biomechanical and/or hemodynamiccharacteristics (e.g., axial plaque stress, wall shear stress, radiusgradient, etc.) for points on the target patient's geometric model. Inone embodiment, step 908 may include using the trained machine learningalgorithm obtained from step 714 in method 700, as depicted in FIG. 7.In one embodiment, step 908 may include using the patient-specificparameters obtained from step 904 for one or more points on thepatient-specific geometric model when applying the trained machinelearning algorithm to predict hemodynamic characteristics for thosepoints. The machine learning algorithm may take many forms, including,but not limited to, a multi-layer perceptron, multivariate regression,deep learning, support vector machines, random forests, k-nearestneighbors, Bayes networks, etc. Step 908 may use processing devices ofserver systems 106.

In one embodiment, step 910 may include outputting the hemodynamiccharacteristics (e.g., axial plaque stress, wall shear stress, etc.)and/or results of the machine learning algorithm into an electronicstorage medium of server systems 106. The hemodynamic characteristicsmay be those obtained from the application of a trained machine learningalgorithm in step 908. In one embodiment, the output may includepatient-specific characteristics other than hemodynamic characteristics.In one embodiment, step 910 may further include monitoring the risk of apatient and/or assessing treatment strategies based on the output.

Alternatively, or in addition to steps 808 and 908 of methods 800 and900, respectively, biomechanical and/or hemodynamic characteristics maybe predicted, computed, or derived from the patient-specific parametersusing computational flow dynamics and/or Hagen-Poiseuille assumptions.For example, the wall shear stress may be derived by computing thecross-sectional area at a point i (A_(i)) on a vasculature or geometricmodel, computing the effective lumen diameter (D_(i)), where

${D_{i} = {2\sqrt{\frac{A_{i}}{\pi}}}},$

and estimating the wall shear stress at the point i (WSS_(i)) using apressure gradient (PG_(i)) computed from a flow simulation ormeasurements, where

${WSS}_{i} = {{PG}_{i} \cdot {\frac{D_{i}}{4}.}}$

In another example, the axial plaque stress may be derived by computingthe radius gradient at a point i (RG_(i)) over an interval (ds), where

${{RG}_{i} = {\left( {\sqrt{\frac{A_{i + 1}}{\pi}} - \sqrt{\frac{A_{i}}{\pi}}} \right)/{s}}},$

and estimating the axial plaque stress over a point i, APS_(i) using aradius gradient (RG_(i)) computed from flow simulation or measurements(e.g., as in 206B and 208B of FIG. 2B), where

${APS}_{i} = {{{RG}_{analytic} \cdot {Pressure}} = {{\frac{1}{N}{\sum\limits_{1}^{N}{{{RG}_{i} \cdot {Pressure}}\mspace{14mu} {and}\mspace{14mu} {APS}_{i}}}} = {{RG}_{ave} \cdot {{Pressure}.}}}}$

In one embodiment, the simplified hemodynamic characteristics may beused to compute more accurate hemodynamic characteristics and/or be usedas part of a machine learning algorithm to obtain the hemodynamiccharacteristics for points on the geometric model where the simplifiedhemodynamic characteristics may not be known.

FIG. 10 is a block diagram of an exemplary method for estimatingbiomechanical and/or hemodynamic values on one or more points of apatient-specific geometric model using one or more patient-specificparameters, according to an exemplary embodiment of the presentdisclosure. These patient-specific parameters may include, but are notlimited to patient characteristics (e.g., age, gender, etc.),physiological characteristics (e.g., hematocrit level, blood pressure,heart rate, etc.), geometric characteristics (e.g., radius gradient,lumen characteristics, stenosis characteristics, etc.), plaquecharacteristics (e.g., location of plaque, adverse plaquecharacteristics score, plaque burden, presence of napkin ring, intensityof plaque, type of plaque, etc.), simplified hemodynamic characteristics(e.g., wall shear stress and axial plaque stress values derived fromcomputational fluid dynamics), and/or coronary dynamics characteristics(e.g., distensibility of coronary artery over cardiac cycle, bifurcationangle change over cardiac cycle, curvature change over cardiac cycle,etc.). The method 1000 of FIG. 10 may be performed by server systems106, based on information received from physicians 102 and/or thirdparty providers 104 over electronic network 100.

In one embodiment, the method 1000 of FIG. 10 may include a trainingmethod 1002, for training one or more machine learning algorithms basedon patient-specific parameters from numerous patients and measured,estimated, and/or simulated biomechanical and/or hemodynamic values, anda production method 1004 for using the machine learning algorithmresults to predict a target patient's biomechanical and/or hemodynamiccharacteristics.

In one embodiment, training method 1002 may involve acquiring, for eachof a plurality of individuals, e.g., in digital format: (a) apatient-specific geometric model, (b) one or more measured or estimatedpatient-specific parameters, and (c) estimated or simulatedbiomechanical and/or hemodynamic values (e.g., axial plaque stress, wallshear stress, radius gradient, etc.). Training method 1002 may theninvolve, for one or more points in each patient's model, creating afeature vector of the patients' physiological parameters at one or morepoints of a geometric model and associating the feature vector with thevalues of hemodynamic characteristics at those points of the geometricmodel. Training method 1002 may then save the results of the machinelearning algorithm, including feature weights, in a storage device ofserver systems 106. The stored feature weights may define the extent towhich patient-specific parameters and/or anatomical geometry arepredictive of hemodynamic characteristics.

In one embodiment, the production method 1004 may involve estimatingbiomechanical and/or hemodynamic characteristics for a particularpatient, based on results of executing training method 1002. In oneembodiment, production method 1004 may include acquiring, e.g. indigital format: (a) a patient-specific geometric model, and (b) one ormore measured or estimated patient-specific parameters (e.g., patientcharacteristics, physiological characteristics, geometriccharacteristics, plaque characteristics, simplified hemodynamiccharacteristics, and/or coronary dynamics characteristics). For multiplepoints in the patient's geometric model, production method 1004 mayinvolve creating a feature vector of the patient-specific parametersused in the training mode. Production method 1004 may then use savedresults of the machine learning algorithm to produce estimates of thepatient's biomechanical and/or hemodynamic characteristics for eachpoint in the patient-specific geometric model. Finally, productionmethod 1004 may include saving the results of the machine learningalgorithm, including predicted biomechanical and/or hemodynamiccharacteristics, to a storage device of server systems 106.

FIGS. 11A and 11B are block diagrams of exemplary methods, 1100A and1100B, respectively, for using hemodynamic characteristics to monitorrisk and make appropriate clinical decisions, according to an exemplaryembodiment of the present disclosure. Moreover, FIGS. 11A-11B depictembodiments for performing step 308 of making appropriate clinicaldecisions based on the saved hemodynamic characteristics.

Specifically, FIG. 11A depicts a block diagram of method 1100A for usinghemodynamic characteristics to monitor risk and make appropriateclinical decisions in a catheterization laboratory. In one embodiment,step 1102A may include determining whether the fractional flow reserve(FFR) value of the patient is less than or equal to a threshold forfractional flow reserve values (e.g., 0.8). The fractional flow reserveof the patient may be obtained, measured, or derived from the electronicstorage medium and/or by using the embodiments disclosed in the presentdisclosure, which provide systems and methods for estimatingbiomechanical and/or hemodynamic characteristics, including fractionalflow reserve, using patient-specific parameters.

If, subsequent to step 1102A, the fractional flow reserve (FFR) value ofthe patient is less than or equal to the threshold for fractional flowreserve values, e.g., 0.8, then step 1104A may include determiningwhether the stress within a plaque is greater than an ultimate plaquestrength divided by a safety factor (e.g., of two) or whether the axialplaque stress multiplied by the adverse plaque characteristics (APC)score is greater than or equal to a threshold for the product value(e.g., 40,000). If, subsequent to step 1102A, the fractional flowreserve (FFR) value of the patient is greater than the threshold forfractional flow reserve values (e.g., 0.8), then step 1106A may alsoinclude determining whether the stress within a plaque is greater thanan ultimate plaque strength divided by a safety factor (e.g., of two) orwhether the axial plaque stress multiplied by the adverse plaquecharacteristics (APC) score is greater than or equal to a threshold forthe product value, e.g., 40,000.

The adverse plaque characteristics (APC) score can be calculated byconverting measurements of APC (e.g., presence of positive remodeling,napkin ring sign, low Hounsfield unit, or spotty calcification) toordinal variables (e.g., 1, 2, 3, etc.) based on the number of observedtypes of APC or continuous variables (e.g., probability) derived frommachine-learning based classifier (e.g., logistic regression, supportvector machine, etc.). In some embodiments, the adverse plaquecharacteristics may include, for example, atherosclerotic plaquecharacteristics.

If, subsequent to steps 1102A and 1104A, the fractional flow reserve(FFR) is less than or equal to the threshold for fractional flow reservevalues (e.g., 0.8) and either the stress within a plaque is greater thanan ultimate plaque strength divided by a safety factor (e.g., of two) orthe axial plaque stress (APS) multiplied by the adverse plaquecharacteristics (APC) score is greater than or equal to the thresholdfor the product value (e.g., 40,000), then step 1108A may includeperforming a percutaneous coronary intervention (PCI) on the patient.If, subsequent to steps 1102A and 1104A, the fractional flow reserve(FFR) is less than or equal to the threshold for the fractional flowreserve value (e.g., 0.8), but neither the stress within a plaque isgreater than an ultimate plaque strength divided by a safety factor(e.g. 2) nor is the axial plaque stress (APS) multiplied by the adverseplaque characteristics (APC) score greater than or equal to thethreshold for the product value (e.g., 40,000), then step 1110A mayinclude performing a percutaneous coronary intervention (PCI) on thepatient or a close medical follow-up with a strict risk control.

If, subsequent to steps 1102A and 1106A, the fractional flow reserve(FFR) is greater than the threshold for the fractional flow reservevalue (e.g., 0.8) and either the stress within a plaque is greater thanan ultimate plaque strength divided by a safety factor (e.g. 2) or theaxial plaque stress (APS) multiplied by the adverse plaquecharacteristics (APC) score is greater than or equal to the thresholdfor the product value (e.g., 40,000), then step 1112A may includeperforming a percutaneous coronary intervention (PCI) on the patient ora close medical follow-up with a strict risk control. If, subsequent tosteps 1102A and 1106A, the fractional flow reserve (FFR) is greater thanthe threshold for the fractional flow reserve value 0.8, but neither thestress within a plaque is greater than an ultimate plaque strengthdivided by a safety factor (e.g., 2) nor is the axial plaque stress(APS) multiplied by the adverse plaque characteristics (APC) scoregreater than or equal to the threshold for the product value (e.g.,40,000), then step 1114A may include performing a medical treatment.

FIG. 11 B depicts a block diagram of method 1100B for using hemodynamiccharacteristics to monitor risk and make appropriate clinical decisionsin an outpatient clinic. In one embodiment, step 1102B may includedetermining whether a stenosis within the acquired image of a patient(e.g., cCTA) is more than 50%. Information about the stenosis of thepatient may be obtained, measured, or derived from the electronicstorage medium and/or by using the embodiments disclosed in the presentdisclosure, which provide systems and methods for estimatingbiomechanical and/or hemodynamic characteristics using patient-specificparameters.

If, subsequent to step 1102B, the stenosis within the acquired image ofa patient is more than 50%, then step 1104B may include determiningwhether the stress within a plaque is greater than an ultimate plaquestrength divided by a safety factor (e.g., of two) or whether the axialplaque stress multiplied by the adverse plaque characteristics (APC)score greater than or equal to a threshold for the product value (e.g.,40,000). If, subsequent to step 1102B, the stenosis within the acquiredimage of a patient is less than 50%, then step 1106B may also includedetermining whether the stress within a plaque is greater than anultimate plaque strength divided by a safety factor of two or whetherthe axial plaque stress multiplied by the adverse plaque characteristics(APC) score is greater than or equal to a threshold for the productvalue (e.g., 40,000).

If, subsequent to steps 11026 and 11046, the stenosis within theacquired image of a patient is more than 50% and either the stresswithin a plaque is greater than an ultimate plaque strength divided by asafety factor (e.g. of two) or the axial plaque stress (APS) multipliedby the adverse plaque characteristics (APC) score is greater than orequal to the threshold for the product value (e.g., 40,000), then step11086 may include performing an invasive procedure on the patient. If,subsequent to steps 11026 and 11046, the stenosis within the acquiredimage of a patient is more than 50%, but neither the stress within aplaque is greater than an ultimate plaque strength divided by a safetyfactor (e.g. of two) nor is the axial plaque stress (APS) multiplied bythe adverse plaque characteristics (APC) score greater than or equal tothe threshold for the product value (e.g., 40,000), then step 11106 mayinclude performing an invasive procedure on the patient and/orperforming a close medical follow-up with a strict risk control.

If, subsequent to steps 11026 and 11066, the stenosis within theacquired image of a patient is less than 50% and either the stresswithin a plaque is greater than an ultimate plaque strength divided by asafety factor (e.g. two) or the axial plaque stress (APS) multiplied bythe adverse plaque characteristics (APC) score is greater than or equalto the threshold for the product value (e.g., 40,000), then step 11126may include performing a close medical follow-up with a strict riskcontrol on the patient. If, subsequent to steps 11026 and 11066, thestenosis within the acquired image of a patient is less than 50%, butneither the stress within a plaque is greater than an ultimate plaquestrength divided by a safety factor (e.g. 2) nor is the axial plaquestress (APS) multiplied by the adverse plaque characteristics (APC)score greater than or equal to the threshold for the product value(e.g., 40,000), then step 11146 may include performing a medicaltreatment.

FIG. 12 depicts an exemplary method 1200 for determining an exerciseintensity using hemodynamic characteristics based on a simulated orperformed exercise and/or stress test, according to an exemplaryembodiment of the present disclosure.

In one embodiment, step 1202 may include acquiring a patient-specificgeometric model invasively (e.g., OCT, IVUS, etc.) and/or non-invasively(e.g., cCTA). The acquired geometric model may include one or moretarget vessels and/or tissues of a patient and may be saved as a digitalrepresentation in an electronic storage medium. Non-invasive methods forgenerating the geometric model may include performing a cardiac CTimaging of the patient. Invasive methods for generating the geometricmodel may include performing intravascular ultrasound (IVUS) imaging oroptical coherence tomography (OCT) of the target vasculature. Theinvasively and/or non-invasively acquired image may then be segmentedmanually or automatically to identify voxels belonging to the vesselsand/or lumen of interest. Once the voxels are identified, a geometricmodel may be derived (e.g., using marching cubes). In one embodiment,the patient-specific geometric model may include a cardiovascular modelof a specific person and/or a patient's ascending aorta and coronaryartery tree. In another embodiment, the patient-specific geometric modelmay be of a vascular model other than the cardiovascular model. In oneembodiment, the geometric model may be represented as a list of pointsin space (possibly with a list of neighbors for each point) in which thespace may be mapped to spatial units between points (e.g., millimeters).

Step 1204 may include performing and/or simulating an exercise test(e.g., treadmill test) on the patient. In one embodiment, an exercisetest is any aerobic physical exercise that places a patient in astressed physiological condition (e.g., raised heart beat) for asustained period (e.g., more than 5 minutes).

Step 1206 may include obtaining a patient's maximum physiologicalcharacteristics (e.g., hematocrit level, blood pressure, heart rate,etc.) non-invasively using a mobile device. In one embodiment, apatient's maximum physiological characteristics may be obtained when apatient is under a stressed physiological condition, for example, whenthe patient is undergoing the exercise test or immediately thereafter.The physiological characteristics may include, but is not limited to,the blood pressure, heart rate, hematocrit level, and/or anyphysiological measurement or derivation that may be obtainednon-invasively, using a mobile device.

Step 1208A, 1208B, 1208C, 1208D, and 1208E may include obtaining,measuring, or deriving patient-specific parameters (e.g., geometriccharacteristics, plaque characteristics, coronary dynamiccharacteristics, patient characteristics, physiological characteristics,etc.). While the geometric characteristics, plaque characteristics,and/or coronary dynamics characteristics may be pre-acquired fromliterature, patient history, and/or the electronic storage medium, thepatient characteristics and physiological characteristics may beobtained by input and/or extracted from step 1206.

In one embodiment, step 1210 may include determining the biophysicaland/or hemodynamic characteristics (e.g., axial plaque stress, wallshear stress, etc.) using computational fluid dynamics and/or a machinelearning algorithm. In one embodiment, the simplified hemodynamicscharacteristics (e.g., wall shear stress, axial plaque stress, etc.) maybe derived from Hagen-Poiseuille flow assumptions. For example, the wallshear stress may be derived by computing the cross-sectional area at apoint i (A_(i)) on a vasculature, computing the effective lumen diameter(D_(i)), where

${D_{i} = {2\sqrt{\frac{A_{i}}{\pi}}}},$

and estimating the wall shear stress at the point i (WSS_(i)) using apressure gradient (PG_(i)) computed from a flow simulation ormeasurements, where

${WSS}_{i} = {{PG}_{i} \cdot {\frac{D_{i}}{4}.}}$

In another example, the axial plaque stress may be derived by computingthe radius gradient at a point i (RG_(i)) over an interval (ds), where

${{RG}_{i} = {\left( {\sqrt{\frac{A_{i + 1}}{\pi}} - \sqrt{\frac{A_{i}}{\pi}}} \right)/{s}}},$

and estimating APS (APS_(i)) using a radius gradient (RG_(i)) computedfrom flow simulation or measurements (e.g., as in 206B and 208B of FIG.2B), where

${APS}_{i} = {{{RG}_{analytic} \cdot {Pressure}} = {{\frac{1}{N}{\sum\limits_{1}^{N}{{{RG}_{i} \cdot {Pressure}}\mspace{14mu} {and}\mspace{14mu} {APS}_{i}}}} = {{RG}_{ave} \cdot {{Pressure}.}}}}$

In one embodiment, the simplified hemodynamic characteristics may beused to compute more accurate hemodynamic characteristics and/or be usedas part of a machine learning algorithm to obtain the hemodynamiccharacteristics for points on the geometric model where the simplifiedhemodynamic characteristics may not be known.

In one embodiment, step 1210 may include using the patient-specificparameters obtained from step 1208A-E (e.g., patient characteristics,physiological characteristics, geometric characteristics, plaquecharacteristics, simplified hemodynamic characteristics, and/or coronarydynamics characteristics) to form feature vectors to train and applymachine learning algorithm to determine the maximum allowablebiomechanical and/or hemodynamic characteristics. For example, for oneor more points on the geometric model where a simplified maximumallowable hemodynamic characteristics can be calculated usingcomputational fluid dynamics, a feature vector may then be associatedwith the computed maximum allowable hemodynamic characteristics for theone or more points on the geometric model. The feature vectors and theirassociated maximum allowable biomechanical and/or hemodynamiccharacteristics may be used to train a machine learning algorithm thatmay be stored in an electronic storage medium. The trained machinelearning algorithm may be applied to another geometric model usinganother set of patient-specific parameters to derive the maximumallowable biomechanical and/or hemodynamic characteristics for points onthe geometric model.

In one embodiment, step 1212 may include outputting the maximumallowable biomechanical and/or hemodynamic characteristics to anelectronic storage medium and/or display of server systems 106. Thehemodynamic characteristics may be those obtained from the applicationof a trained machine learning algorithm in step 1210. In one embodiment,the output may include patient-specific characteristics other than themaximum allowable hemodynamic characteristics.

In one embodiment, step 1214 may include producing a warning in responseto abnormal values of hemodynamic characteristics (e.g., axial plaquestress, wall shear stress, etc.). In one embodiment, the hemodynamiccharacteristics may be measured, derived, or obtained using the method1300 depicted in FIG. 13, and may be compared to the maximum allowablehemodynamic characteristics that may be measured, derived or obtainedusing method 1200 depicted in FIG. 12.

FIG. 13 is a block diagram of exemplary method 1300 for usingpredetermined exercise intensity (e.g., as in FIG. 12) to monitor riskin patients, according to an exemplary embodiment of the presentdisclosure.

In one embodiment, step 1302 may include acquiring a patient-specificgeometric model invasively (e.g., OCT, IVUS, etc.) and/or non-invasively(e.g., cCTA). The geometric model may be the same as the geometric modelacquired to determine the maximum allowable hemodynamic characteristicsfor the same patient. The acquired geometric model may include one ormore target vessels and/or tissues of a patient and may be saved as adigital representation in an electronic storage medium. Non-invasivemethods for generating the geometric model may include performing acardiac CT imaging of the patient. Invasive methods for generating thegeometric model may include performing intravascular ultrasound (IVUS)imaging or optical coherence tomography (OCT) of the target vasculature.The invasively and/or non-invasively acquired image may then besegmented manually or automatically to identify voxels belonging to thevessels and/or lumen of interest. Once the voxels are identified, ageometric model may be derived (e.g., using marching cubes). In oneembodiment, the patient-specific geometric model may include acardiovascular model of a specific person and/or a patient's ascendingaorta and coronary artery tree. In another embodiment, thepatient-specific geometric model may be of a vascular model other thanthe cardiovascular model. In one embodiment, the geometric model may berepresented as a list of points in space (possibly with a list ofneighbors for each point) in which the space may be mapped to spatialunits between points (e.g., millimeters).

Step 1304 may include obtaining a patient's physiological and/or bloodsupply characteristics (e.g., hematocrit level, blood pressure, heartrate, etc.) using a mobile device. The physiological characteristics mayinclude, but is not limited to, the blood pressure, heart rate,hematocrit level, and/or any physiological measurement or derivationthat may be obtained non-invasively, using a mobile device.

Step 1306A, 1306B, 1306C, 1306D, and 1306E may include obtaining,measuring, or deriving patient-specific parameters (e.g., geometriccharacteristics, plaque characteristics, coronary dynamiccharacteristics, patient characteristics, physiological characteristics,etc.). While the geometric characteristics, plaque characteristics,and/or coronary dynamics characteristics may be pre-acquired fromliterature, patient history, and/or the electronic storage medium, thepatient characteristics and physiological characteristics may beobtained by input and/or extracted from step 1304, using a mobiledevice.

In one embodiment, step 1308 may include determining the patient'scurrent biophysical and/or hemodynamic characteristics (e.g., axialplaque stress, wall shear stress, etc.) using computational fluiddynamics and/or a machine learning algorithm.

In one embodiment, the simplified hemodynamics characteristics (e.g.,wall shear stress, axial plaque stress, etc.) may be derived fromHagen-Poiseuille flow assumptions. For example, the wall shear stressmay be derived by computing the cross-sectional area at a point i(A_(i)) on a vasculature, computing the effective lumen diameter(D_(i)), where

${D_{i} = {2\sqrt{\frac{A_{i}}{\pi}}}},$

and estimating the wall shear stress at the point i (WSS_(i)) using apressure gradient (PG_(i)) computed from a flow simulation ormeasurements, where

${WSS}_{i} = {{PG}_{i} \cdot {\frac{D_{i}}{4}.}}$

In another example, the axial plaque stress may be derived by computingthe radius gradient at a point i (RG_(i)) over an interval (ds), where

${{RG}_{i} = {\left( {\sqrt{\frac{A_{i + 1}}{\pi}} - \sqrt{\frac{A_{i}}{\pi}}} \right)/{s}}},$

and estimating APS (APS_(i)) using a radius gradient (RG_(i)) computedfrom flow simulation or measurements (e.g., as in 206B and 208B of FIG.2B), where

${APS}_{i} = {{{RG}_{analytic} \cdot {Pressure}} = {{\frac{1}{N}{\sum\limits_{1}^{N}{{{RG}_{i} \cdot {Pressure}}\mspace{14mu} {and}\mspace{14mu} {APS}_{i}}}} = {{RG}_{ave} \cdot {{Pressure}.}}}}$

In one embodiment, the simplified hemodynamic characteristics may beused to compute more accurate hemodynamic characteristics and/or be usedas part of a machine learning algorithm to obtain the hemodynamiccharacteristics for points on the geometric model where the simplifiedhemodynamic characteristics may not be known.

In one embodiment, step 1308 may include using the patient-specificparameters obtained from step 1208A-E (e.g., patient characteristics,physiological characteristics, geometric characteristics, plaquecharacteristics, simplified hemodynamic characteristics, and/or coronarydynamics characteristics) to form feature vectors to train and applymachine learning algorithm to determine the current biomechanical and/orhemodynamic characteristics of the patient. For example, for one or morepoints on the geometric model where a simplified hemodynamiccharacteristics can be calculated using computational fluid dynamics, afeature vector may then be associated with the computed hemodynamiccharacteristics for the one or more points on the geometric model. Thefeature vectors and their associated biomechanical and/or hemodynamiccharacteristics may be used to train a machine learning algorithm thatmay be stored in an electronic storage medium. The trained machinelearning algorithm may be applied to another geometric model usinganother set of patient-specific parameters to derive the biomechanicaland/or hemodynamic characteristics for points on the geometric model.

Step 1310 may include obtaining the patient's maximum allowablehemodynamic characteristics. In one embodiment, a patient's maximumphysiological characteristics may be obtained from prior tests and/orfrom method 1200 depicted in FIG. 12, while a patient is undergoing theexercise test or immediately after an exercise test. In otherembodiments, a patient's maximum physiological characteristics may besimulated and/or obtained from literature (e.g., a patient's medicalrecords). A patient's maximum physiological characteristics may beobtained from or stored in an electronic storage system of server system106.

In one embodiment, step 1312 may include comparing the currenthemodynamic characteristics of a patient with the maximum allowablehemodynamic characteristics of a patient. In one embodiment, thecomparison may involve determining whether the current hemodynamiccharacteristics is greater than, less than, or within an optimal rangebelow the maximum allowable hemodynamic characteristics.

In one embodiment, step 1314 may include producing a warning in responseto abnormal values of hemodynamic characteristics. For example, if thecurrent measured, derived, or obtained axial plaque stress is above anoptimal range or value for the maximum allowable hemodynamiccharacteristic, a warning may be provided to the patient or physician.In one embodiment, the warning may be a signal or prompt provided on themobile device of the patient or physician. In one embodiment, acumulative history of the measurements or estimations of the hemodynamiccharacteristics of a patient and/or a cumulative history of whetherthese measurements or estimations were abnormal and/or above an optimalrange of the maximum allowable hemodynamic characteristic may be savedto an electronic storage medium of server system 106.

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the invention being indicated by the following claims.

What is claimed is:
 1. A computer implemented method for estimatingvalues of hemodynamic forces acting on plaque or lesions, the methodcomprising: receiving one or more patient-specific parameters of atleast a portion of a patient's vasculature that is prone to plaqueprogression, rupture, or erosion; constructing a patient-specificgeometric model of at least a portion of a patient's vasculature that isprone to plaque progression, rupture, or erosion, using the received oneor more patient-specific parameters; estimating, using one or moreprocessors, the values of hemodynamic forces at one or more points onthe patient-specific geometric model, using the patient-specificparameters and geometric model by measuring, deriving, or obtaining oneor more of a pressure gradient and a radius gradient; and outputting theestimated values of hemodynamic forces to an electronic storage medium.2. The computer implemented method of claim 1, wherein constructing apatient-specific geometric model includes: receiving one or more imagesof a patient anatomy comprising at least a portion of a vasculature thatmay be prone to a plaque progression, rupture, or erosion, using, one ormore of, computerized tomography, optical coherence tomography,intravascular ultrasound imaging, intravascular pressure-wire, motorizedpull-back system, angiogram, or a combination thereof; receiving orupdating the one or more patient-specific parameters, using the receivedone or more images regarding patient anatomy; deriving apatient-specific geometric model, by identifying one or more portions ofa patient's vasculature on the received one or more images; and updatingthe patient specific geometric model based on the received one or morepatient-specific parameters.
 3. The computer implemented method of claim1, wherein estimating values of hemodynamic forces at one or more pointson the geometric model includes, one or more of: measuring, deriving, orobtaining a pressure gradient, radius gradient, or both from, one ormore of, the patient-specific parameters, computerized tomography,optical coherence tomography, intravascular ultrasound imaging,intravascular pressure-wire, or flow simulations of the geometric model;and measuring, deriving, or obtaining the axial plaque stress using, oneor more of, radius gradient and the pressure gradient.
 4. The computerimplemented method of claim 1, wherein the patient-specific parametersmay include one or more measured, derived, or obtained physiologicalcharacteristics, including, one or more of, blood pressure, heart rate,hematocrit level, or a combination thereof.
 5. The computer implementedmethod of claim 1, wherein the patient-specific parameters may includeone or more measured, derived, or obtained geometric characteristics,including, one or more of, radius gradient, lumen characteristics,stenosis characteristics, or a combination thereof.
 6. The computerimplemented method of claim 1, wherein the patient-specific parametersmay include one or more measured, derived, or obtained plaquecharacteristics, including, one or more of, the location of a plaque,adverse plaque characteristics score, plaque burden, presence of napkinring, intensity of plaque, type of plaque, or a combination thereof. 7.The computer implemented method of claim 1, wherein the patient-specificparameters may include one or more measured, derived, or obtainedcoronary dynamics characteristics, including, one or more of, thedistensibility of coronary artery over cardiac cycle, bifurcation anglechange over cardiac cycle, curvature change over cardiac cycle, or acombination thereof.
 8. The computer implemented method of claim 1,wherein the patient-specific parameters may include one or more patientcharacteristics, including, one or more of, age, gender, weight, height,medical history, or a combination thereof.
 9. The computer implementedmethod of claim 1, wherein the hemodynamic forces acting on a plaque,lesion, or one or more points on the geometric model include, one ormore of, the traction within a vessel, traction force, pressure,pressure gradient, wall shear stress, axial plaque stress, radiusgradient, and/or fractional flow reserve (FFR), or a combinationthereof.
 10. The computer implemented method of claim 1, wherein thepatient-specific geometric model of a patient anatomy include, one ormore of: a coronary vascular model; a cerebral vascular model; aperipheral vascular model; a hepatic vascular model; a renal vascularmodel; a visceral vascular model; or any vascular model with vesselssupplying blood that may be prone to plaque formation.
 11. The computerimplemented method of claim 1, wherein receiving or calculating one ormore patient-specific parameters includes acquiring a digitalrepresentation of one or more patient-specific parameters usingnon-invasive measurement techniques, including, one or more of,performing a cardiac CT imaging of the patient in the end diastole phaseof the cardiac cycle, measuring through a mobile devices and/orsmartphones or a non-invasive physiological measurement device affixedto the mobile device and/or smart phone, or a combination thereof. 12.The computer implemented method of claim 1, wherein receiving orcalculating one or more patient-specific parameters includes acquiring adigital representation of one or more patient-specific parameters usinginvasive measurement techniques, including, performing intravascularultrasound (IVUS) imaging, optical coherence tomography (OCT), pressurewire measurements, intravascular motorized pull-back measurements, or acombination thereof.
 13. The computer implemented method of claim 1,further comprising: predicting the risk of plaque progression, rupture,or erosion based on the estimated values of hemodynamic forces at theone or more points on the geometric model; and assessing treatmentoptions of a patient, based on the predicted risk of plaque progression,rupture, or erosion.
 14. The computer implemented method of claim 1,wherein outputting the estimated values of hemodynamic forces to anelectronic storage medium includes outputting, one or more of, theestimated values of hemodynamic forces, the patient-specific parameters,or the geometric model, to a display.
 15. A system for predicting plaqueprogression, rupture, or erosion using one or more hemodynamic forcesacting on lesions or plaque, the system comprising: a data storagedevice storing instructions for estimating hemodynamic forces; and aprocessor configured to execute the instructions to perform a methodincluding: receiving one or more patient-specific parameters of at leasta portion of a patient's vasculature that is prone to plaqueprogression, rupture, or erosion; constructing a patient-specificgeometric model of at least a portion of a patient's vasculature that isprone to plaque progression, rupture, or erosion, using the received oneor more patient-specific parameters; estimating, using one or moreprocessors, the values of hemodynamic forces at one or more points onthe patient-specific geometric model, using the patient-specificparameters and geometric model by measuring, deriving, or obtaining oneor more of a pressure gradient and a radius gradient; and outputting theestimated values of hemodynamic forces to an electronic storage medium.16. The system of claim 15, wherein constructing a patient-specificgeometric model includes: receiving one or more images of a patientanatomy comprising at least a portion of a vasculature that may be proneto a plaque progression, rupture, or erosion, using, one or more of,computerized tomography, optical coherence tomography, intravascularultrasound imaging, intravascular pressure-wire, motorized pull-backsystem, angiogram, or a combination thereof; receiving or updating theone or more patient-specific parameters, using the received one or moreimages of the patient anatomy; deriving a patient-specific geometricmodel, by identifying one or more portions of a patient's vasculature onthe received one or more images; and updating the patient specificgeometric model based on the received one or more patient-specificparameters.
 17. The system of claim 15, wherein estimating values ofhemodynamic forces at one or more points on the geometric modelincludes, one or more of: measuring, deriving, or obtaining a pressuregradient, radius gradient, or both from, one or more of, thepatient-specific parameters, computerized tomography, optical coherencetomography, intravascular ultrasound imaging, intravascularpressure-wire, or flow simulations of the geometric model; andmeasuring, deriving, or obtaining the axial plaque stress using, one ormore of, radius gradient and the pressure gradient.
 18. The system ofclaim 15, wherein the patient-specific parameters may include, one ormore of, physiological characteristics, geometric characteristics,plaque characteristics, coronary dynamics characteristics, or patientcharacteristics.
 19. The system of claim 15, wherein the hemodynamicforces acting on a plaque, lesion, or one or more points on thegeometric model include, one or more of, the traction within a vessel,traction force, pressure, pressure gradient, wall shear stress, axialplaque stress, radius gradient, and/or fractional flow reserve (FFR), ora combination thereof.
 20. A non-transitory computer readable medium foruse on a computer system containing computer-executable programminginstructions for estimating values of hemodynamic forces acting onplaque or lesions, the method comprising: receiving one or morepatient-specific parameters of at least a portion of a patient'svasculature that is prone to plaque progression, rupture, or erosion;constructing a patient-specific geometric model of at least a portion ofa patient's vasculature that is prone to plaque progression, rupture, orerosion, using the received one or more patient-specific parameters;estimating, using one or more processors, the values of hemodynamicforces at one or more points on the patient-specific geometric model,using the patient-specific parameters and geometric model by measuring,deriving, or obtaining one or more of a pressure gradient and a radiusgradient; and outputting the estimated values of hemodynamic forces toan electronic storage medium.